Approximate maximum likelihood estimation for population genetic inference

Bertl Johanna, Ewing Gregory, Kosiol Carolin and Futschik Andreas ()
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Bertl Johanna: Department of Molecular Medicine (MOMA), Aarhus University Hospital, Palle Juul-Jensens Boulevard 99, 8200 Aarhus N, Denmark
Ewing Gregory: École polytechnique fédérale de Lausanne, 1015 Lausanne, Switzerland
Kosiol Carolin: Centre for Biological Diverstity, University of St Andrews, St Andrews, Fife KY16 9TH, UK
Futschik Andreas: Department of Applied Statistics, Johannes Kepler University Linz, Altenberger Straße 69, 4040 Linz, Austria

Statistical Applications in Genetics and Molecular Biology, 2017, vol. 16, issue 5-6, 291-312

Abstract: In many population genetic problems, parameter estimation is obstructed by an intractable likelihood function. Therefore, approximate estimation methods have been developed, and with growing computational power, sampling-based methods became popular. However, these methods such as Approximate Bayesian Computation (ABC) can be inefficient in high-dimensional problems. This led to the development of more sophisticated iterative estimation methods like particle filters. Here, we propose an alternative approach that is based on stochastic approximation. By moving along a simulated gradient or ascent direction, the algorithm produces a sequence of estimates that eventually converges to the maximum likelihood estimate, given a set of observed summary statistics. This strategy does not sample much from low-likelihood regions of the parameter space, and is fast, even when many summary statistics are involved. We put considerable efforts into providing tuning guidelines that improve the robustness and lead to good performance on problems with high-dimensional summary statistics and a low signal-to-noise ratio. We then investigate the performance of our resulting approach and study its properties in simulations. Finally, we re-estimate parameters describing the demographic history of Bornean and Sumatran orang-utans.

Keywords: approximate inference; isolation-migration model; maximum likelihood estimation; orang-utans; population genetics; stochastic approximation (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1515/sagmb-2017-0016

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